INTRODUCTORY STATISTICS

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1 INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore

2 CONTENTS PART I BASIC PROBABILITY AND STATISTICS 1 The Nature of Statistics 1-1 Random Sampling: A Political Poll 1-2 Randomized Experiments: Testing a Hospital Routine Observational Studies vs. Randomized Experiments Brief Outline of the Book 20 Chapter 1 Summary 20 2 Descriptive Statistics 2-1 Frequency Tables and Graphs Center of a Distribution Spread of a Distribution Statistics by Computer Linear Transformations Calculations Using Relative Frequencies The Use and Misuse of Graphs 53 Chapter 2 Summary 64 3 Probability 3-1 Introduction Probability Models Compound Events Conditional Probability Independence Bayes Theorem: Tree Reversal Other Views of Probability 99 Chapter 3 Summary Probability Distributions 4-1 Discrete Random Variables Mean and Variance The Binomial Distribution Continuous Distributions The Normal Distribution A Function of a Random Variable 134 *4-7 Expected Value in Bidding 141 Chapter 4 Summary Two Random Variables Distributions A Function of Two Random Variables Covariance Linear Combination of Two Random Variables 170 Chapter 5 Summary 176 Review Problems (Chapters 1-5) 182 PART II INFERENCE FOR MEANS AND PROPORTIONS Sampling Random Sampling Moments of the Sample Mean The Shape of the Sampling Distribution Proportions (Percentages) 207 *6-5 Small-Population Sampling 215 *6-6 Monte Carlo 218 Chapter 6 Summary Point Estimation Populations and Samples Efficiency of Unbiased Estimators Efficiency of Biased and Unbiased Estimators 239 *7-4 Consistent Estimators 244 Chapter 7 Summary 248 XIII

3 XIV CONTENTS 8 Confidence Intervals A Single Mean Small-Sample t Difference in Two Means, Independent Samples Difference in Two Means, Matched Samples Proportions 273 *8-6 The Bootstrap 277 Chapter 8 Summary Hypothesis Testing Hypothesis Testing Using Confidence Intervals p-value (One-Sided) Classical Hypothesis Tests 300 *9-4 Classical Tests Reconsidered 306 *9-5 Operating Characteristics Curve (OCC) 310 *9-6 Two-Sided Tests 314 Chapter 9 Summary Analysis of Variance (ANOVA) One-Way ANOVA Two-Way ANOVA Confidence Intervals 343 Chapter 10 Summary 346 Review Problems (Chapters 6-10) Confidence Intervals and Tests for p Predicting Vat a Given Level of X Extending the Model 389 Chapter 12 Summary Multiple Regression Why Multiple Regression? The Regression Model and Its OLS Fit Confidence Intervals and Statistical Tests Regression Coefficients as Multiplication Factors 410 *13-5 Simple and Multiple Regression Compared 417 *13-6 Path Analysis 424 Chapter 13 Summary Regression Extensions Dummy (0-1) Variables Analysis of Variance (ANOVA) by Regression Simplest Nonlinear Regression 449 *14-4 Nonlinearity Removed by Logs 452 *14-5 Diagnosis by Residual Plots 461 Chapter 14 Summary Correlation 474 PART III REGRESSION: RELATING TWO OR MORE VARIABLES Fitting a Line Introduction Ordinary Least Squares (OLS) Advantages of OLS and WLS 366 Chapter 11 Summary Simple Correlation Correlation and Regression 15-3 The Two Regression Lines Correlation in Multiple Regression Multicollinearity 501 Chapter 15 Summary 506 Review Problems (Chapters 11-15) Simple Regression The Regression Model Sampling Variability 375 PART IV TOPICS IN CLASSICAL AND BAYESIAN INFERENCE 515

4 CONTENTS XV 16 Nonparametric and Robust Statistics (Requires Chapter 9) Introduction: Mean or Median? Sign Test for the Median Confidence Interval for the Median Wilcoxon Rank Test Rank Tests in General Runs Test for Independence Robust Statistics: Trimming and Weighting 536 Chapter 16 Summary Chi-Square Tests (Requires Chapter 9) x 2 Tests for Multinomials: Goodness of Fit x 2 Tests for Independence: Contingency Tables 555 Chapter 17 Summary 561 *18 Maximum Likelihood Estimation (Requires Chapter 7) Introduction MLE for Some Familiar Cases MLE for the Uniform Distribution MLE in General 576 Chapter 18 Summary 579 *19 Bayesian Inference (Requires Chapter 8) Posterior Distributions The Population Proportion The Mean ^ in a Normal Model The Slope /3 in Normal Regression Bayesian Shrinkage Estimates Classical and Bayesian Estimates Compared 615 Chapter 19 Summary 615 *20 Bayesian Decision Theory (Requires Chapter 19) 20-1 Maximizing Gain (or Minimizing Loss) Point Estimation as a Decision Classical and Bayesian Statistics Compared 633 Chapter 20 Summary 635 * Appendixes 2-2 Careful Approximation of the Median 638 N 2-5 Effects of a Liriear Transformation* Proofs Probability as Axiomatic Mathematics Easier Formula for o- 2 : Proof Binomial Formula: Proof Calculus for Continuous Distributions Independent Implies Uncorrelated: Proof Linear Combinations: Proofs Central Limit Theorem Continuity Correction: Graphical Explanation 643 ( 7-2 Standard Error of X Consistency: Careful Definition Standard Error of (X, - X 2 ): Proof Confidence Interval for w. Derivation of Graph A More Exact p-value for Proportions Breakdown of Total SS: Proof Two-Way ANOVA, Breakdown of Total SS: Proof ANOVA Is Much More Than Just Testing H o Lines and Planes Least-Squares Formulas: Proofs The Moments of fa: Proofs and Discussion A One-sided or Two-sided Test?

5 XVI CONTENTS 12-4 Confidence Intervals above X o : Proofs Solution of a Set of Simultaneous Equations Direct Plus Indirect Relation: Proof Log Regression Handles a Multiplicative Error Term Correlation in Chapter 15 Agrees with Chapter ANOVA and r 2 : Proofs MLE for Some Familiar Cases: Proofs Bayesian Confidence Interval fortr Proof Posterior Distribution of fi in a Normal Model: Proof Posterior Distribution of j8 in Normal Regression: Proof Bayesian Shrinkage Confidence Intervals 662 Tables 663 References 679 Answers to Odd-Numbered Problems 685 Glossary of Common Symbols 699 Index of Examples and Problems 703 index 705

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